Price elasticity of demand
- Price elasticity (midpoint)
- E = (ΔQ/Q̄)/(ΔP/P̄)
- Elastic / inelastic
- |E| > 1 elastic, |E| < 1 inelastic
- Revenue
- TR = P·Q
Microeconomics: cram pack
Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Price elasticity of demandMedium
When the price of a ticket changes from €5.00 to €6.00, weekly sales change from 1200 to 1100. Use the midpoint (arc) method to find the price elasticity of demand E.
P1 = €5.00P2 = €6.00Q1 = 1200Q2 = 1100
E =
2.Price elasticity of demandHard
The demand for a product is Q = 150 − 5P, with P in euros. At which price P is total revenue as large as possible?
Q = 150 − 5P
P = €
3.Economics conceptsMedium
Nominal GDP grew by 5% and the GDP deflator rose by 2%. Real GDP grew by approximately:
- A7%
- B2.5%
- C3%
- D10%
4.Economics conceptsHard
A monopolist maximises profit where:
- AAverage cost is at its minimum
- BMarginal revenue equals marginal cost
- CTotal revenue is at its maximum
- DPrice equals marginal cost
3Solutions
1.Price elasticity of demand
Answer: E = −0.4783
Price elasticity of demand measures how strongly the quantity demanded reacts to price: E = (% change in quantity)/(% change in price). It is negative for normal goods. |E| > 1 is elastic (revenue falls when price rises), |E| < 1 is inelastic.
Relative change in quantity
(1100 − 1200)/((1200 + 1100)/2) = −100/1150 = −0.08696
Relative change in price
(6 − 5)/((5 + 6)/2) = 1/5.5 = 0.1818
Elasticity
E = −0.08696/0.1818 = −0.4783
Answer
E = −0.4783
2.Price elasticity of demand
Answer: P = 15 €
Price elasticity of demand measures how strongly the quantity demanded reacts to price: E = (% change in quantity)/(% change in price). It is negative for normal goods. |E| > 1 is elastic (revenue falls when price rises), |E| < 1 is inelastic.
Revenue as a function of price
R = P·(150 − 5P) = 150P − 5P²
Set the derivative to zero
dR/dP = 150 − 10P = 0
P = 150/10 = €15.00
Answer
P = €15.00
At this price E = −1: demand is unit elastic.
3.Economics concepts
Answer: C · 3%
Why this is the answer
Subtracting the rise in prices from nominal growth gives real growth of roughly 5% − 2% = 3%.
Answer
C · 3%
4.Economics concepts
Answer: B · Marginal revenue equals marginal cost
Why this is the answer
Profit is maximised where MR = MC. For a monopolist, price is above MR, so P > MC, causing a deadweight loss.
Answer
B · Marginal revenue equals marginal cost
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